More on the Tensorial Central Charges in N=1 Supersymmetric Gauge Theories (BPS Wall Junctions and Strings)

TL;DR

This paper investigates central charges in N=1 supersymmetric gauge theories, focusing on BPS solitons like strings and junctions, and identifies conditions for their existence, including at weak and strong coupling regimes.

Contribution

It provides a general expression for central charges in four-dimensional gauge theories and proves that BPS strings at weak coupling only occur in supersymmetric electrodynamics with Fayet-Iliopoulos term.

Findings

Only supersymmetric electrodynamics with Fayet-Iliopoulos term admits BPS strings at weak coupling.

Ambiguity in the (1/2,1/2) central charge is addressed and resolved.

Potential existence of BPS strings at strong coupling in N=2 theories is discussed.

Abstract

We study the central extensions of the N=1 superalgebras relevant to the soliton solutions with the axial geometry - strings, wall junctions, etc. A general expression valid in any four-dimensional gauge theory is obtained. We prove that the only gauge theory admitting BPS strings at weak coupling is supersymmetric electrodynamics with the Fayet-Iliopoulos term. The problem of ambiguity of the (1/2,1/2) central charge in the generalized Wess-Zumino models and gauge theories with matter is addressed and solved. A possibility of existence of the BPS strings at strong coupling in N=2 theories is discussed. A representation of different strings within the brane picture is presented.